Measurement of the Shape of the Boson-Transverse Momentum Distribution
in p
p ! Z=
! e
e
X Events Produced at
p
s
1:96 TeV
V. M. Abazov,36B. Abbott,76M. Abolins,66B. S. Acharya,29M. Adams,52T. Adams,50E. Aguilo,6S. H. Ahn,31 M. Ahsan,60G. D. Alexeev,36G. Alkhazov,40A. Alton,65,*G. Alverson,64G. A. Alves,2M. Anastasoaie,35L. S. Ancu,35
T. Andeen,54S. Anderson,46B. Andrieu,17M. S. Anzelc,54Y. Arnoud,14M. Arov,61M. Arthaud,18A. Askew,50 B. A˚ sman,41A. C. S. Assis Jesus,3O. Atramentov,50C. Autermann,21C. Avila,8C. Ay,24F. Badaud,13A. Baden,62 L. Bagby,53B. Baldin,51D. V. Bandurin,60S. Banerjee,29P. Banerjee,29E. Barberis,64A.-F. Barfuss,15P. Bargassa,81
P. Baringer,59J. Barreto,2J. F. Bartlett,51U. Bassler,18D. Bauer,44S. Beale,6A. Bean,59M. Begalli,3M. Begel,72 C. Belanger-Champagne,41L. Bellantoni,51A. Bellavance,51J. A. Benitez,66S. B. Beri,27G. Bernardi,17R. Bernhard,23 I. Bertram,43M. Besanc¸on,18R. Beuselinck,44V. A. Bezzubov,39P. C. Bhat,51V. Bhatnagar,27C. Biscarat,20G. Blazey,53
F. Blekman,44S. Blessing,50D. Bloch,19K. Bloom,68A. Boehnlein,51D. Boline,63T. A. Bolton,60G. Borissov,43 T. Bose,78A. Brandt,79R. Brock,66G. Brooijmans,71A. Bross,51D. Brown,82N. J. Buchanan,50D. Buchholz,54 M. Buehler,82V. Buescher,22V. Bunichev,38S. Burdin,43,†S. Burke,46T. H. Burnett,83C. P. Buszello,44J. M. Butler,63
P. Calfayan,25S. Calvet,16J. Cammin,72W. Carvalho,3B. C. K. Casey,51N. M. Cason,56H. Castilla-Valdez,33 S. Chakrabarti,18D. Chakraborty,53K. M. Chan,56K. Chan,6A. Chandra,49F. Charles,19,**E. Cheu,46F. Chevallier,14
D. K. Cho,63S. Choi,32B. Choudhary,28L. Christofek,78T. Christoudias,44S. Cihangir,51D. Claes,68Y. Coadou,6 M. Cooke,81W. E. Cooper,51M. Corcoran,81F. Couderc,18M.-C. Cousinou,15S. Cre´pe´-Renaudin,14D. Cutts,78
M. C´ wiok,30H. da Motta,2A. Das,46G. Davies,44K. De,79S. J. de Jong,35E. De La Cruz-Burelo,65
C. De Oliveira Martins,3J. D. Degenhardt,65F. De´liot,18M. Demarteau,51R. Demina,72D. Denisov,51S. P. Denisov,39 S. Desai,51H. T. Diehl,51M. Diesburg,51A. Dominguez,68H. Dong,73L. V. Dudko,38L. Duflot,16S. R. Dugad,29 D. Duggan,50A. Duperrin,15J. Dyer,66A. Dyshkant,53M. Eads,68D. Edmunds,66J. Ellison,49V. D. Elvira,51Y. Enari,78
S. Eno,62P. Ermolov,38H. Evans,55A. Evdokimov,74V. N. Evdokimov,39A. V. Ferapontov,60T. Ferbel,72F. Fiedler,24 F. Filthaut,35W. Fisher,51H. E. Fisk,51M. Ford,45M. Fortner,53H. Fox,23S. Fu,51S. Fuess,51T. Gadfort,83C. F. Galea,35 E. Gallas,51E. Galyaev,56C. Garcia,72A. Garcia-Bellido,83V. Gavrilov,37P. Gay,13W. Geist,19D. Gele´,19C. E. Gerber,52
Y. Gershtein,50D. Gillberg,6G. Ginther,72N. Gollub,41B. Go´mez,8A. Goussiou,56P. D. Grannis,73H. Greenlee,51 Z. D. Greenwood,61E. M. Gregores,4G. Grenier,20Ph. Gris,13J.-F. Grivaz,16A. Grohsjean,25S. Gru¨nendahl,51 M. W. Gru¨newald,30J. Guo,73F. Guo,73P. Gutierrez,76G. Gutierrez,51A. Haas,71N. J. Hadley,62P. Haefner,25 S. Hagopian,50J. Haley,69I. Hall,66R. E. Hall,48L. Han,7K. Hanagaki,51P. Hansson,41K. Harder,45A. Harel,72
R. Harrington,64J. M. Hauptman,58R. Hauser,66J. Hays,44T. Hebbeker,21D. Hedin,53J. G. Hegeman,34 J. M. Heinmiller,52A. P. Heinson,49U. Heintz,63C. Hensel,59K. Herner,73G. Hesketh,64M. D. Hildreth,56R. Hirosky,82 J. D. Hobbs,73B. Hoeneisen,12H. Hoeth,26M. Hohlfeld,22S. J. Hong,31S. Hossain,76P. Houben,34Y. Hu,73Z. Hubacek,10 V. Hynek,9I. Iashvili,70R. Illingworth,51A. S. Ito,51S. Jabeen,63M. Jaffre´,16S. Jain,76K. Jakobs,23C. Jarvis,62R. Jesik,44
K. Johns,46C. Johnson,71M. Johnson,51A. Jonckheere,51P. Jonsson,44A. Juste,51D. Ka¨fer,21E. Kajfasz,15 A. M. Kalinin,36J. R. Kalk,66J. M. Kalk,61S. Kappler,21D. Karmanov,38P. Kasper,51I. Katsanos,71D. Kau,50R. Kaur,27
V. Kaushik,79R. Kehoe,80S. Kermiche,15N. Khalatyan,51A. Khanov,77A. Kharchilava,70Y. M. Kharzheev,36 D. Khatidze,71H. Kim,32T. J. Kim,31M. H. Kirby,54M. Kirsch,21B. Klima,51J. M. Kohli,27J.-P. Konrath,23M. Kopal,76
V. M. Korablev,39A. V. Kozelov,39D. Krop,55T. Kuhl,24A. Kumar,70S. Kunori,62A. Kupco,11T. Kurcˇa,20J. Kvita,9 F. Lacroix,13D. Lam,56S. Lammers,71G. Landsberg,78P. Lebrun,20W. M. Lee,51A. Leflat,38F. Lehner,42J. Lellouch,17
J. Leveque,46P. Lewis,44J. Li,79Q. Z. Li,51L. Li,49S. M. Lietti,5J. G. R. Lima,53D. Lincoln,51J. Linnemann,66 V. V. Lipaev,39R. Lipton,51Y. Liu,7Z. Liu,6L. Lobo,44A. Lobodenko,40M. Lokajicek,11P. Love,43H. J. Lubatti,83 A. L. Lyon,51A. K. A. Maciel,2D. Mackin,81R. J. Madaras,47P. Ma¨ttig,26C. Magass,21A. Magerkurth,65P. K. Mal,56
H. B. Malbouisson,3S. Malik,68V. L. Malyshev,36H. S. Mao,51Y. Maravin,60B. Martin,14R. McCarthy,73 A. Melnitchouk,67A. Mendes,15L. Mendoza,8P. G. Mercadante,5M. Merkin,38K. W. Merritt,51J. Meyer,22,xA. Meyer,21 T. Millet,20J. Mitrevski,71J. Molina,3R. K. Mommsen,45N. K. Mondal,29R. W. Moore,6T. Moulik,59G. S. Muanza,20 M. Mulders,51M. Mulhearn,71O. Mundal,22L. Mundim,3E. Nagy,15M. Naimuddin,51M. Narain,78N. A. Naumann,35 H. A. Neal,65J. P. Negret,8P. Neustroev,40H. Nilsen,23H. Nogima,3A. Nomerotski,51S. F. Novaes,5T. Nunnemann,25
V. O’Dell,51D. C. O’Neil,6G. Obrant,40C. Ochando,16D. Onoprienko,60N. Oshima,51J. Osta,56R. Otec,10 G. J. Otero y Garzo´n,51M. Owen,45P. Padley,81M. Pangilinan,78N. Parashar,57S.-J. Park,72S. K. Park,31J. Parsons,71 R. Partridge,78N. Parua,55A. Patwa,74G. Pawloski,81B. Penning,23M. Perfilov,38K. Peters,45Y. Peters,26P. Pe´troff,16
M. Petteni,44R. Piegaia,1J. Piper,66M.-A. Pleier,22P. L. M. Podesta-Lerma,33,‡V. M. Podstavkov,51Y. Pogorelov,56 M.-E. Pol,2P. Polozov,37B. G. Pope,66A. V. Popov,39C. Potter,6W. L. Prado da Silva,3H. B. Prosper,50S. Protopopescu,74 J. Qian,65A. Quadt,22,xB. Quinn,67A. Rakitine,43M. S. Rangel,2K. Ranjan,28P. N. Ratoff,43P. Renkel,80S. Reucroft,64
P. Rich,45M. Rijssenbeek,73I. Ripp-Baudot,19F. Rizatdinova,77S. Robinson,44R. F. Rodrigues,3M. Rominsky,76 C. Royon,18P. Rubinov,51R. Ruchti,56G. Safronov,37G. Sajot,14A. Sa´nchez-Herna´ndez,33M. P. Sanders,17A. Santoro,3
G. Savage,51L. Sawyer,61T. Scanlon,44D. Schaile,25R. D. Schamberger,73Y. Scheglov,40H. Schellman,54 P. Schieferdecker,25T. Schliephake,26C. Schwanenberger,45A. Schwartzman,69R. Schwienhorst,66J. Sekaric,50 H. Severini,76E. Shabalina,52M. Shamim,60V. Shary,18A. A. Shchukin,39R. K. Shivpuri,28V. Siccardi,19V. Simak,10
V. Sirotenko,51P. Skubic,76P. Slattery,72D. Smirnov,56J. Snow,75G. R. Snow,68S. Snyder,74S. So¨ldner-Rembold,45 L. Sonnenschein,17A. Sopczak,43M. Sosebee,79K. Soustruznik,9M. Souza,2B. Spurlock,79J. Stark,14J. Steele,61 V. Stolin,37D. A. Stoyanova,39J. Strandberg,65S. Strandberg,41M. A. Strang,70M. Strauss,76E. Strauss,73R. Stro¨hmer,25
D. Strom,54L. Stutte,51S. Sumowidagdo,50P. Svoisky,56A. Sznajder,3M. Talby,15P. Tamburello,46A. Tanasijczuk,1 W. Taylor,6J. Temple,46B. Tiller,25F. Tissandier,13M. Titov,18V. V. Tokmenin,36T. Toole,62I. Torchiani,23T. Trefzger,24 D. Tsybychev,73B. Tuchming,18C. Tully,69P. M. Tuts,71R. Unalan,66S. Uvarov,40L. Uvarov,40S. Uzunyan,53B. Vachon,6 P. J. van den Berg,34R. Van Kooten,55W. M. van Leeuwen,34N. Varelas,52E. W. Varnes,46I. A. Vasilyev,39M. Vaupel,26
P. Verdier,20L. S. Vertogradov,36M. Verzocchi,51F. Villeneuve-Seguier,44P. Vint,44P. Vokac,10E. Von Toerne,60 M. Voutilainen,68,kR. Wagner,69H. D. Wahl,50L. Wang,62M. H. L. S Wang,51J. Warchol,56G. Watts,83M. Wayne,56
M. Weber,51G. Weber,24A. Wenger,23,{N. Wermes,22M. Wetstein,62A. White,79D. Wicke,26G. W. Wilson,59 S. J. Wimpenny,49M. Wobisch,61D. R. Wood,64T. R. Wyatt,45Y. Xie,78S. Yacoob,54R. Yamada,51M. Yan,62T. Yasuda,51 Y. A. Yatsunenko,36K. Yip,74H. D. Yoo,78S. W. Youn,54J. Yu,79A. Zatserklyaniy,53C. Zeitnitz,26T. Zhao,83B. Zhou,65
J. Zhu,73M. Zielinski,72D. Zieminska,55A. Zieminski,55,**L. Zivkovic,71V. Zutshi,53and E. G. Zverev38 (The D0 Collaboration)
1Universidad de Buenos Aires, Buenos Aires, Argentina 2LAFEX, Centro Brasileiro de Pesquisas Fı´sicas, Rio de Janeiro, Brazil
3Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil 4Universidade Federal do ABC, Santo Andre´, Brazil
5Instituto de Fı´sica Teo´rica, Universidade Estadual Paulista, Sa˜o Paulo, Brazil 6University of Alberta, Edmonton, Alberta, Canada,
Simon Fraser University, Burnaby, British Columbia, Canada, York University, Toronto, Ontario, Canada,
and McGill University, Montreal, Quebec, Canada
7University of Science and Technology of China, Hefei, People’s Republic of China 8Universidad de los Andes, Bogota´, Colombia
9Center for Particle Physics, Charles University, Prague, Czech Republic 10Czech Technical University, Prague, Czech Republic
11Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic 12Universidad San Francisco de Quito, Quito, Ecuador
13Laboratoire de Physique Corpusculaire, IN2P3-CNRS, Universite´ Blaise Pascal, Clermont-Ferrand, France 14Laboratoire de Physique Subatomique et de Cosmologie, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France
15CPPM, IN2P3-CNRS, Universite´ de la Me´diterrane´e, Marseille, France
16Laboratoire de l’Acce´le´rateur Line´aire, IN2P3-CNRS et Universite´ Paris-Sud, Orsay, France 17LPNHE, IN2P3-CNRS, Universite´s Paris VI and VII, Paris, France
18DAPNIA/Service de Physique des Particules, CEA, Saclay, France
19IPHC, Universite´ Louis Pasteur et Universite´ de Haute Alsace, CNRS, IN2P3, Strasbourg, France 20IPNL, Universite´ Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universite´ de Lyon, Lyon, France
21III. Physikalisches Institut A, RWTH Aachen, Aachen, Germany 22Physikalisches Institut, Universita¨t Bonn, Bonn, Germany 23Physikalisches Institut, Universita¨t Freiburg, Freiburg, Germany
24Institut fu¨r Physik, Universita¨t Mainz, Mainz, Germany 25Ludwig-Maximilians-Universita¨t Mu¨nchen, Mu¨nchen, Germany 26Fachbereich Physik, University of Wuppertal, Wuppertal, Germany
27Panjab University, Chandigarh, India 28Delhi University, Delhi, India
30University College Dublin, Dublin, Ireland 31Korea Detector Laboratory, Korea University, Seoul, Korea
32SungKyunKwan University, Suwon, Korea 33CINVESTAV, Mexico City, Mexico
34FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands 35Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands
36Joint Institute for Nuclear Research, Dubna, Russia 37Institute for Theoretical and Experimental Physics, Moscow, Russia
38Moscow State University, Moscow, Russia 39Institute for High Energy Physics, Protvino, Russia 40Petersburg Nuclear Physics Institute, St. Petersburg, Russia
41Lund University, Lund, Sweden, Royal Institute of Technology and Stockholm University, Stockholm, Sweden,
and Uppsala University, Uppsala, Sweden
42Physik Institut der Universita¨t Zu¨rich, Zu¨rich, Switzerland 43Lancaster University, Lancaster, United Kingdom
44Imperial College, London, United Kingdom 45University of Manchester, Manchester, United Kingdom
46University of Arizona, Tucson, Arizona 85721, USA
47Lawrence Berkeley National Laboratoryand University of California, Berkeley, California 94720, USA 48California State University, Fresno, California 93740, USA
49University of California, Riverside, California 92521, USA 50Florida State University, Tallahassee, Florida 32306, USA 51Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
52University of Illinois at Chicago, Chicago, Illinois 60607, USA 53Northern Illinois University, DeKalb, Illinois 60115, USA
54Northwestern University, Evanston, Illinois 60208, USA 55Indiana University, Bloomington, Indiana 47405, USA 56University of Notre Dame, Notre Dame, Indiana 46556, USA
57Purdue University Calumet, Hammond, Indiana 46323, USA 58Iowa State University, Ames, Iowa 50011, USA 59University of Kansas, Lawrence, Kansas 66045, USA 60Kansas State University, Manhattan, Kansas 66506, USA 61Louisiana Tech University, Ruston, Louisiana 71272, USA 62University of Maryland, College Park, Maryland 20742, USA
63Boston University, Boston, Massachusetts 02215, USA 64Northeastern University, Boston, Massachusetts 02115, USA
65University of Michigan, Ann Arbor, Michigan 48109, USA 66Michigan State University, East Lansing, Michigan 48824, USA
67University of Mississippi, University, Mississippi 38677, USA 68University of Nebraska, Lincoln, Nebraska 68588, USA 69Princeton University, Princeton, New Jersey 08544, USA 70State University of New York, Buffalo, New York 14260, USA
71Columbia University, New York, New York 10027, USA 72University of Rochester, Rochester, New York 14627, USA 73State University of New York, Stony Brook, New York 11794, USA
74Brookhaven National Laboratory, Upton, New York 11973, USA 75Langston University, Langston, Oklahoma 73050, USA 76University of Oklahoma, Norman, Oklahoma 73019, USA 77Oklahoma State University, Stillwater, Oklahoma 74078, USA
78Brown University, Providence, Rhode Island 02912, USA 79University of Texas, Arlington, Texas 76019, USA 80Southern Methodist University, Dallas, Texas 75275, USA
81Rice University, Houston, Texas 77005, USA 82University of Virginia, Charlottesville, Virginia 22901, USA
83University of Washington, Seattle, Washington 98195, USA
(Received 5 December 2007; published 11 March 2008) We present a measurement of the shape of the Z=boson transverse momentum (q
T) distribution in
pp ! Z= ! ee X events at a center-of-mass energy of 1.96 TeV using 0:98 fb1of data collected
with the D0 detector at the Fermilab Tevatron collider. The data are found to be consistent with the resum-mation prediction at low qT, but above the perturbative QCD calculation in the region of qT> 30 GeV=c.
Using events with qT< 30 GeV=c, we extract the value of g2, one of the nonperturbative parameters for
the resummation calculation. Data at large boson rapidity y are compared with the prediction of re-summation and with alternative models that employ a resummed form factor with modifications in the small Bjorken x region of the proton wave function.
DOI:10.1103/PhysRevLett.100.102002 PACS numbers: 13.85.t, 12.38.Qk, 13.38.Dg
A complete understanding of weak vector boson pro-duction is essential for maximizing the sensitivity to new physics at hadron colliders. Studies of the Z= boson production play a particularly valuable role in that its kinematics can be precisely determined through measure-ment of its leptonic decays. Throughout this Letter, we use the notation ‘‘Z boson’’ to mean ‘‘Z= boson,’’ unless specified otherwise.
Z boson production also serves as an ideal testing ground for predictions of quantum chromodynamics (QCD), since the boson’s transverse momentum, qT, can be measured over a wide range of values and can be correlated with its rapidity. At large qT (approximately
greater than 30 GeV=c), the radiation of a single parton with large transverse momentum dominates the cross sec-tion, and fixed-order perturbative QCD (pQCD) calcula-tions [1], currently available at next-to-next-to leading order (NNLO) [2], should yield reliable predictions. At lower qT, multiple soft-gluon emission can not be ne-glected, and the fixed-order perturbation calculation no longer gives accurate results. A soft-gluon resummation technique developed by Collins, Soper, and Sterman (CSS) [3] gives reliable predictions in the low-qT region. A prescription has been proposed [4] for matching the low-and high-qT regions in order to provide a continuous prediction for all values of qT. The CSS resummation formalism allows the inclusion of contributions from large logarithms of the form lnnq2
T=Q2 to all orders of
pertur-bation theory in an effective resummed form factor, where Q2represents the invariant mass corresponding to the
four-momentum transfer. The CSS resummation can be done either in impact parameter (b) space or in transverse mo-mentum (qT) space. In the case of b-space resummation,
this form factor can be parameterized with the following nonperturbative function first introduced by Brock, Landry, Nadolsky, and Yuan (BLNY) [5]:
SNPb; Q2 g 1 g2ln Q 2Q0 g1g3ln100xixj b2; (1) where xi and xj are the fractions of the incident hadron
momenta carried by the colliding partons, Q0 is a scale
typical of the onset of nonperturbative effects, and g1, g2,
and g3 are phenomenological nonperturbative parameters
that must be obtained from fits to the data. The Z boson qT
distribution at the Fermilab Tevatron is by far most sensi-tive to the value of g2and quite insensitive to the value of g3. Thus, a measurement of the Z boson qT spectrum can
be used to test this formalism and to determine the value of
g2.
Recent studies of data from deep inelastic scattering (DIS) experiments [6,7] indicate that the resummed form factor in the above equation may need to be modified for processes involving a small-x parton in the initial state. Reference [8] indicates how such a modification would influence the qT distributions of vector and Higgs bosons produced in hadronic collisions. A wider qT distribution is predicted for Z bosons with large rapidity (called ‘‘small-x broadening’’). Z bosons produced at the Tevatron in the rapidity range 2 < jyj < 3 probe processes involving a parton with 0:002 < x < 0:006, and can be used to test the modified form factor at small x.
Zboson qTdistributions have been published previously
by the CDF [9] and D0 [10] collaborations using about 100 pb1of data atps 1:8 TeV. In this Letter, we report a new measurement with larger statistics and improved precision. This measurement is also the first to present a qT distribution for large-rapidity Z bosons.
The data sample used in this measurement was collected using a set of inclusive single-electron triggers with the D0 detector [11] at the Fermilab Tevatron collider, and the integrated luminosity is 980 60 pb1[12].
Our selection criteria for Z bosons require two isolated electromagnetic clusters that have a shower shape consis-tent with that of an electron. Electron candidates are re-quired to have transverse momentum greater than 25 GeV=c. The electron pairs must have a reconstructed invariant mass 70 < Mee < 110 GeV=c2. If an event has
both its candidate electrons in the central calorimeter (CC events), each electron must be spatially matched to a reconstructed track. Because the tracking efficiency de-creases with rapidity in the endcap region, events with one or two endcap calorimeter electron candidates (CE and EE events, respectively) are required to have at least one electron with a matching track. After these require-ments, 23 959 CC, 30 344 CE, and 9598 EE events are selected; 5412 of these have a Z boson with jyj > 2.
Electron identification efficiencies are measured using a combination of data and aGEANT-based [13] simulation of the D0 detector. The electron identification efficiencies are measured from Z data. The dependence of the overall selection efficiency on the Z boson qT is parameterized
from the GEANTsimulation. A measurement of this shape from the data agrees well with the simulation within sta-tistical uncertainties.
The dominant backgrounds are from photon plus jet events and di-jet events, with photons and jets
misidenti-fied as electrons. The kinematic properties of these events are obtained from events that satisfy most of the Z selec-tion criteria, but fail the electron shower shape require-ment. The normalization of the background is obtained by fitting to a sum of a signal shape obtained from a parame-terized simulation of the detector response and the invari-ant mass distribution from the background sample to the invariant mass distribution of the data sample. The back-ground fractions are 1:30 0:14%, 8:55 0:26%, and 4:71 0:30% for CC, CE, and EE events, respectively. Other backgrounds are negligible.
The data are corrected for acceptances within a range of generated Z masses of 40 to 200 GeV=c2, and for selection
efficiencies using a parameterized simulation. We use
RESBOS [14] as the event generator which incorporates the resummation calculation in b-space using the BLNY parameterization for low qT and a NLO pQCD calculation for high qT. We usePHOTOS[15] to simulate the effects of final state photon radiation. The overall acceptance times efficiency falls slowly from a value of 0.27 at low qT to a
minimum of 0.19 at qT 40 GeV=c and slowly increases for larger qT.
The measured spectrum is further corrected for detector resolution effects using the RUN(Regularized Unfolding) program [16] to obtain the true differential cross section. Its performance was verified by comparing the true and unfolded spectrum generated using pseudoexperiments. The measured Z qT resolution is about 2 GeV=c; the bin
width we choose is 2:5 GeV=c for qT< 30 GeV=c. The typical correlation between adjacent bins is around 30%. Due to limited statistics, the chosen bin width is 10 GeV=c for 30 < qT< 100 GeV=c and 40 GeV=c for 100 < qT <
260 GeV=c.
Systematic uncertainties on the unfolded qT spectrum arise from uncertainties on the electron energy calibration, the electron energy resolution, the dependence of the over-all selection efficiency on qT, and the effect of parton
distribution functions (PDFs) on the acceptance. The un-certainties on the unfolded spectrum are estimated from the resulting change when the smearing parameters are varied within their uncertainties. CTEQ 6.1M is used as the default PDF. Uncertainties due to the PDFs are estimated using the procedure described in Ref. [17]. The uncertainty due to the choice of unfolding parameters in the RUN
program is also estimated and included in the final system-atic uncertainty.
The final results in the qT< 30 GeV=c range are shown in Fig.1for the inclusive sample and for the sample with jyj > 2. Each data point is plotted at the average value of the expected distribution over the bin [18]. For the theo-retical calculation, we useRESBOSwith published values of the nonperturbative parameters [5]. Good agreement be-tween data and the prediction is observed for all rapidity ranges, which indicates that the BLNY parameterization works well for the low qT region.
Zboson events produced at large rapidities (jyj > 2) are also used to test the small-x prediction. We compare data with the theoretical predictions with and without the form factor as modified from studies of small-x DIS data [8]. All curves are normalized to 1 for qT< 30 GeV=c. The de-fault values for the parameters g1, g2, and g3 [5] obtained
from large-x data are used. The 2=d:o:f: between the data
and theRESBOScalculation using the default parameters is 0:8=1 for qT< 5 GeV=c and 11:1=11 for qT < 30 GeV=c,
while that for the modified calculation is 5:7=1 for qT<
5 GeV=c and 31:9=11 for qT < 30 GeV=c. It remains to be seen if retuning of the nonperturbative parameters could improve the agreement for the modified calculations.
Figure2shows the measured differential cross section in the range qT< 260 GeV=c compared to (1) the RESBOS
calculation with its default parameters [5], (2)RESBOSwith a NLO to NNLO K factor by Arnold and Reno [19] incorporated into RESBOS by its authors, (3) a pQCD (GeV/c) T * q γ Z/ 0 5 10 15 20 25 30 (GeV/c) T /dqσ d× σ 1/ 0.02 0.04 0.06 0.08 RESBOS DØ data DØ, 0.98 fb (a) (GeV/c) T * q γ Z/ 0 5 10 15 20 25 30 -1 (GeV/c) T /dqσ d× σ 1/ 0.02 0.04 0.06 0.08 0.1 |y|>2 RESBOS with small-x effect RESBOS without small-x effect DØ data
DØ, 0.98 fb-1
(b)
FIG. 1 (color online). The normalized differential cross section as a function of qT for (a) the inclusive sample and (b) the sample with Z boson jyj > 2 with qT< 30 GeV=c. The points are the data, the solid curve is the RESBOSprediction, and the dashed line in (b) is the prediction from the form factor modified after studies of small-x DIS data.
calculation at NNLO [2] using the MRST 2001 NNLO PDF set [20] divided by the NNLO calculation of the total cross section [21], and (4) the NNLO calculation but rescaled to the data at qT 30 GeV=c. The agreement between data andRESBOS, with or without the K factor, is good for qT < 30 GeV=c. At higher values of qT, the data
are not in agreement with theRESBOScalculation. The data
agree better with the NNLO calculation and RESBOS
pre-diction with the Arnold-Reno K factor, but agrees best when the NNLO results are rescaled by a factor of 1.25 so that they match the data at qT 30 GeV=c. This in-dicates that the shape from these calculations agrees with the data, and that the source of the discrepancy is in the normalization. Table I summarizes the measured values for each qT bin together with statistical and systematic uncertainties.
The CSS model parameter most sensitive to the shape at low qT (qT< 30 GeV=c) is g2. In a fit, we fix other phenomenological parameters to the values obtained in Ref. [5] and only vary g2. A minimum 2=d:o:f: of 9=11
between the model and the inclusive data for qT<
30 GeV=c is found when g2 0:77 0:06 GeV=c2.
In conclusion, we have measured the normalized differ-ential spectrum,1 dqd
T, for Z boson events produced in p p collisions at ps 1:96 TeV with boson mass 40 < M < 200 GeV=c2 and q
T< 260 GeV=c. This represents the
highest center-of-mass energy measurement of this quan-tity over the largest phase space available to date. The overall uncertainty of this measurement has been reduced compared with the previous measurements. We find that for qT< 30 GeV=c, the CSS resummation model used in
RESBOS describes the data very well at all rapidities. Our
data with jyj > 2 disfavor a variant of this model that incorporates an additional small-x form factor when g1, g2, and g3 from large-x data is used. Using the BLNY
parameterization for events with qT< 30 GeV=c, we
ob-tain g2 0:77 0:06 GeV=c2, which is comparable
with the current world average value [5]. We observe a disagreement between our data and NNLO calculations in the region qT > 30 GeV=c, where our distribution is higher than predicted by a factor of 1.25. However, the
TABLE I. The normalized differential cross section for Z events produced in bins of qT. The first uncertainty is statistical, and the second is systematic.
hqTi (GeV=c) 1= d=dqT GeV=c1 1.1 5:32 0:13 0:24 102 4.0 8:08 0:12 0:19 102 6.2 6:33 0:11 0:14 102 8.7 4:43 0:09 0:11 102 11.3 3:15 0:08 0:08 102 13.7 2:46 0:07 0:06 102 16.2 1:86 0:06 0:05 102 18.7 1:42 0:05 0:05 102 21.3 1:09 0:04 0:03 102 23.7 9:40 0:40 0:20 103 26.4 6:90 0:30 0:20 103 28.5 5:50 0:30 0:10 103 34.6 3:90 0:10 0:10 103 44.6 2:10 0:07 0:06 103 54.6 1:10 0:05 0:03 103 64.6 7:30 0:40 0:20 104 73.4 4:20 0:30 0:20 104 85.4 2:50 0:20 0:10 104 95.1 1:60 0:17 0:08 104 117.5 6:00 0:50 0:30 105 157.5 1:10 0:20 0:07 105 195.5 3:00 1:00 0:30 106 245.5 7:10 6:10 0:60 107 (GeV/c) T * q γ Z/ 0 50 100 150 200 250 -1 (GeV/c) T /dqσ d× σ 1/ -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 DØ 0.98 fb-1 (a) RESBOS RESBOS+KF NNLO Rescaled NNLO DØ data (GeV/c) T * q γ Z/ 1 10 102 (Data-Theory)/Theory -0.5 0 0.5 1 DØ 0.98 fb-1 (b) RESBOS RESBOS+KF NNLO Rescaled NNLO
FIG. 2 (color online). The normalized differential cross section as a function of qTcompared to four theoretical calculations for (a) the entire range measured and (b) the fractional differences between data and the theoretical predictions. The four theoretical calculations areRESBOSwith its default parameters,RESBOSwith a NLO to NNLO K factor by Arnold and Reno, the NNLO calculation by Melnikov and Petriello, and the NNLO calcula-tion but rescaled to data at qT 30 GeV=c.
NNLO calculation agrees in shape with our data when normalized at qT 30 GeV=c.
We thank C. Balazs, Q. H. Cao, P. Nadolsky, F. Petriello, and C. P. Yuan for many useful discussions. We thank the staffs at Fermilab and collaborating institutions, and ac-knowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France); FASI, Rosatom and RFBR (Russia); CAPES, CNPq, FAPERJ, FAPESP, and FUNDUNESP (Brazil); DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); KRF and KOSEF (Korea); CONICET and UBACyT (Argentina); FOM (The Netherlands); Science and Technology Facilities Council (United Kingdom); MSMT and GACR (Czech Republic); CRC Program, CFI, NSERC, and WestGrid Project (Canada); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); CAS and CNSF (China); Alexander von Humboldt Foundation; and the Marie Curie Program.
*Visitor from Augustana College, Sioux Falls, SD, USA.
†Visitor from The University of Liverpool, Liverpool,
United Kingdom.
‡Visitor from ICN-UNAM, Mexico City, Mexico. xVisitor from II. Physikalisches Institut,
Georg-August-University Go¨ttingen, Germany.
k
Visitor from Helsinki Institute of Physics, Helsinki, Finland.
{
Visitor from Universita¨t Zu¨rich, Zu¨rich, Switzerland.
**Deceased.
[1] P. B. Arnold and M. H. Reno, Nucl. Phys. B 319, 37 (1989); R. J. Gonsalves, J. Pawlowski, and C-F. Wai, Phys. Rev. D 40, 2245 (1989).
[2] K. Melnikov and F. Petriello, Phys. Rev. D 74, 114017 (2006).
[3] J. Collins, D. Soper, and G. Sterman, Nucl. Phys. B 250, 199 (1985).
[4] P. B. Arnold and R. Kauffman, Nucl. Phys. B 349, 381 (1991).
[5] F. Landry et al., Phys. Rev. D 67, 073016 (2003). The values are g1 0:21 0:01 GeV=c2, g2
0:680:010:02GeV=c2, g
3 0:60:050:04, Q0 1:6 GeV=c.
[6] P. Nadolsky, D. R. Stump, and C. P. Yuan, Phys. Rev. D 61, 014003 (1999); 64, 059903(E) (2001).
[7] P. Nadolsky, D. R. Stump, and C. P. Yuan, Phys. Rev. D 64, 114011 (2001).
[8] S. Berge et al., Phys. Rev. D 72, 033015 (2005). [9] T. Affolder et al. (CDF Collaboration), Phys. Rev. Lett. 84,
845 (2000).
[10] B. Abbott et al. (D0 Collaboration), Phys. Rev. D 61, 032004 (2000); B. Abbott et al. (D0 Collaboration), Phys. Rev. Lett. 84, 2792 (2000).
[11] V. Abazov et al. (D0 Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 565, 463 (2006).
[12] T. Andeen et al., Fermilab Report No. FERMILAB-TM-2365, 2007.
[13] R. Brun and F. Carminati, CERN Program Library Long Writeup Report No. W5013, 1993 (unpublished). [14] C. Balazs and C. P. Yuan, Phys. Rev. D 56, 5558 (1997). [15] E. Barberio and Z. Was, Comput. Phys. Commun. 79, 291
(1994).
[16] V. Blobel, The RUNmanual, Regularized Unfolding for High-Energy Physics Experiments, OPAL Technical Note Report No. TN361, 1996.
[17] J. Pumplin et al., J. High Energy Phys. 07 (2002) pp. 012; D. Stump et al., J. High Energy Phys. 10 (2003) 046. [18] G. D. Lafferty and T. R. Wyatt, Nucl. Instrum. Methods
Phys. Res., Sect. A 355, 541 (1995).
[19] P. B. Arnold and M. H. Reno, Nucl. Phys. B 319, 37 (1989); 330, 284(E) (1990).
[20] A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne, Phys. Lett. B 531, 216 (2002).
[21] R. Hamberg, W. van Neerven, and T. Matsuura, Nucl. Phys. B 359, 343 (1991); 644, 403(E) (2002).
